function [ltol,err_ltol] = Verify_ltol(ltol) 
        err_ltol = 1; 
        if isempty(ltol),  
            ltol = 0.1;
        elseif ~isreal(ltol) | ltol<=0, 
            disp('ltol must be a positive real number!');  
            return 
        end
        err_ltol = 0;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% End of Verify_ltol %%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%